Beam Testing

This write up is about testing the beam that was designed and built in the last three projects. This write up will show the expected results, actual results, and the reasons why the two did or did not match. The calculations will be both on paper calculations and from the beam calculator. Here are the results:

Firstly, the beam could not deflect more than 0.1 inch at a concentrated load of 250 lbs. The beam also had to be no more than 2 x 2 inches with a length of 24 inches.

The first step of testing the beam was to do some rough calculations. These are the ones from before I built the beam:

Rough calculations

This shows the on paper calculations and results. It also shows the results from the online calculator that was made previously. There is a fair bit of difference in between the two. The paper calculations gave that the inertia would be 0.821 in^4 and a deflection of .0253 inches. The calculator stated that the inertia would be .685 in^4 and a deflection of .0304 inches. The projected weight, according to the calculator, should approximately be 160 grams. The paper calculations are less accurate due to rounding in between steps. This should be the main source of error.

The beam was already built and needed to be tested. The beam had to be tested in the FabLab and one of the TAs was required to help or at least supervise. Firstly, the beam had to be weighed. There was an electronic scale at the FabLab. I brought the beam in on two separate days, a rainy day and a dry, sunny day. The first day the beam weighed 221.5 grams and the second day it weighed 175.5 grams. The change was astonishing, 40 grams of difference. This is due to how porous basswood is. It can readily absorb water. Now that the beam was weighed, testing the deflection was next. Here are two pictures of the beam in the testing apparatus:

Front view

Side view

The apparatus is simply an A-frame with roller supports and a downwards facing hydraulic jack, which and was operated with a socket wrench.. The jack provides a concentrated load, the same type as the calculations. There is also a dial gauge underneath the beam, it is visible in the first picture. The beam is placed in and the span was set. The rollers were already 18 inches apart, which is the correct span. The whole apparatus was clamped down to the table so that it could not move.

There is a small weight sensor between the jack and the beam. The sensor uses a USB connection with a computer to display how much force is applied to the beam. The sensor was ratted to 500 lb and if the beam was to be destroyed, the senor needed to be removed.

Onto the testing. The results were recorded by the TA who was helping to run the apparatus. Here are the results of the 2 x 2 by 3/16 thick basswood I-beam:

Weight of beam: 175.5 grams

Beam width: 1.97 inches

Beam height: 2.07 inches

Weight applied at 0.1 inch of deflection: 219 lbs

Deflection at 250 lbs: 0.12 inches

Pass or fail: failed

The beam did not pass all of the tests even though the calculations showed that it would. It was 0.07 inches too tall and deflected 0.02 inches too much. The calculations were incorrect. I believe that main source of error was the density of this bass wood. This basswood is rather thin, so any deviance in grain structure or pattern at all would cause major problems. I did try to pick the 'cleanest' wood, without blemish or knots, that could be found. However, the densities of materials are typically measured with large blocks of the material, not thin sheets. I should have realized this sooner and tested these specific pieces, but I did not.

The beam did pass the weight test, even though this was not an actual requirement. The beam was 24.5 grams under the implied weight restriction, which is pretty good. But it was still 15.5 grams over the projected weight. The 0.07 inches of extra height could have been corrected with light sanding on the tops of both flanges. However, the 0.07 inches was due to a slight gap while the glue cured and would not effect the deflection significantly. The beam was also 0.03 inches under the 2 inch restriction.

I am generally pleased with the results, though slightly disappointed that the beam failed the test. But it is still impressive that 3/16 inch basswood can support well over 250 lbs. If I could redo this project I would definitely test the density of the wood by finding the volume and weight. I would also test the deflection of the wood and see if it would pass. If I did go up to 1/4 inch wood I believe that the beam would pass the deflection test, but fail the weight restrictions. The aforementioned deflection calculations were significantly off, but the weight was also incorrect. This happened because the glue was not included with the calculations. An extra 10 - 15 grams should make up the difference of weight, so roughly 5 - 7.5 grams per glue joint.

Another fun project with some cool gadgets and calculations.